Palaeontologia Electronica - The Polly Lab et al... · PALAEO-ELECTRONICA.ORG 3 genetics of fluctuating asymmetry. An estimate of the variance between right and left teeth relative

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Using left-right asymmetry to estimate non-genetic variation invole teeth (Arvicolinae, Muridae, Rodentia)

P. David Polly, Laura Killick, and Mark Ruddy

ABSTRACT

Arvicoline rodents, which are important index fossils for late Cenozoic terrestrialdeposits, are often said to have the greatest amount of dental variation of any mam-mal. If true, if that variation is environmental (ecophenotypic) in nature, and if variationwithin species is greater than between species, then the scientific basis of taxonomicidentifications of these common fossils is questionable. We used left-right asymmetryin the shape of the lower first molar of four arvicoline species as a measure of the envi-ronmental (non-genetic) component of variance within vole species. Using both Eigen-shape and semilandmark (Procrustes) analysis, we found that environmental varianceaccounted for about 10%-30% of within-species variance, suggesting heritabilities (h2)of 0.71 to 0.89 for molar tooth shape. However, the magnitude of this non-genetic vari-ance was considerably smaller than that found between individuals belonging to thesame species and nearly an order of magnitude smaller than differences between spe-cies. It is unlikely that environmental variance or within-species variation regularly con-found species-level taxonomic identifications of vole teeth.

P. David Polly, Department of Geological Sciences, Indiana University,1001 E. 10th Street, Bloomington, IN 47401 USA, [email protected] Killick, Department of Anthropology, University of Durham, 43 Old Elvet, Durham DH1 3HN, United Kingdom, [email protected] Ruddy, Department of Geography, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom, [email protected]

KEY WORDS: ecomorphology; fluctuating asymmetry; geometric morphometrics; morphological evolu-tion; teeth

INTRODUCTION

Voles and lemmings (Arvicolinae, Muridae,Rodentia) are sometimes said to have more dentalvariation than any other mammal (e.g., Yablokov1974; Carleton 1985). Variation can manifest itself

at different hierarchical levels, notably betweenspecies (or clades) and within species (or popula-tions). High levels of variation between species arean advantage for the study of fossil taxa because itmakes species easily distinguishable from one

PE Article Number: 14.3.41ACopyright: Palaeontological Association November 2011Submission: 15 June 2007. Acceptance: 1 August 2011

Polly, P. David, Killick, Laura, and Ruddy, Mark. 2011. Using left-right asymmetry to estimate non-genetic variation in vole teeth (Arvicolinae, Muridae, Rodentia). Palaeontologia Electronica Vol. 14, Issue 3; 41A:12p; palaeo-electronica.org/2011_3/24_polly/index.html

POLLY ET AL.: PLASTICITY IN VOLE TEETH

another. Such inter-specific variation, which issometimes called disparity, is known to be animportant phenomenon in arvicoline rodents. Thedistinctive, rapidly evolving dental morphology ofvoles and lemmings make them important indexfossils for late Cenozoic terrestrial biostratigraphy(e.g., Fejfar 1976; Repenning 1987; Maul et al.1998; Bell et al. 2004). Conversely, variation withinspecies is generally a disadvantage for the study offossil taxa because it makes species difficult todiagnose. Such intra-specific variation is alsoknown to be common in arvicolines, especially inthe anterior cap of the lower molars (e.g., Hinton1926; Van der Muelen 1973; Carleton 1985; Jaar-ola et al. 2004). High intra-specific variation can bean especial problem if it is coupled with low inter-specific variation because that combination leadsto morphological overlap between species, hinder-ing accurate identification of fossils and potentiallyleading to erroneous biostratigraphic or biogeo-graphic interpretations.

Variation within species can be divided intogenetic and environmental components of variance(e.g., Lynch and Walsh 1998). Quantitative geneti-cists describe this division using the equation

P = G + E, (Equation 1)

where P is the phenotypic variance, or the variationwe see in morphological structures such as teeth,G is the genetic variance, or the variation in a spe-cies that is passed from parent to offspring, and Eis the environmental variance, or the variation thatis directly determined by local environment regard-less of parentage. G represents heritable variation,regardless of whether the heritability has a directone-to-one correspondence to genes coded on theDNA or a less direct but equally heritable develop-mental system whose morphogenetic outcomesare determined by the effects directly heritable reg-ulator genes. E represents variation from all non-genetic sources, regardless of whether the sourcesare internal or external developmental noise,norms of reaction, or epigenetic variation. E is aquantitative genetics formulation of what is oftenknown as morphological or ecophenotypic plastic-ity in the palaeontological literature (e.g., Newell1948; Hughes 1991).

Generally speaking, the palaeontologicalstudy of taxonomy, species relationships, rates ofevolution, and evolutionary patterns depends onvariation being primarily genetic in nature becausenon-genetic variation may obscure underlyinggenetic and, therefore, evolutionary patterns. Con-clusions about taxonomy or evolution could be mis-guided if environmental variance is great enough to

cause undetected similarity among distantlyrelated species or difference among conspecificpopulations. These potentially pernicious environ-mental effects, which are also called ecopheno-typic or plastic variation, manifest themselves overthe lifetime of an individual and should not be con-fused with evolutionary adaptation to environment,which is a consequence of genetic variance andnatural selection over tens, hundreds, thousands,or millions of generations (e.g., Kratochvíl 1983).For these reasons, palaeontologists have often dis-tinguished between the genetic and environmentalcomponents of variance in skeletal traits as a toolfor better understanding evolutionary and environ-mental change (e.g., Schopf 1976; Pachut 1987;Hadly 1997; Polly 2004; Kavanagh et al. 2007).

Because the teeth of voles and lemmings arenoted for both their inter- and intra-specific varia-tion and because their teeth are so important forbiostratigraphic interpretation, it is of interest toknow the extent to which this variation is genetic.The proportion of genetic and environmental com-ponents of phenotypic variance is usually deter-mined by large breeding experiments that allow thesimilarity between parents and their offspring to bemeasured directly or indirectly through ‘commongarden’ experiments that bring genetically diverseindividuals into the same environmental conditionsin order to measure directly the resulting similari-ties (e.g., Lynch and Walsh 1998). Such experi-ments are expensive and time consuming even forliving species, and in any case they cannot beapplied to fossil animals.

Non-genetic variance can be estimated lesslaboriously by measuring asymmetry between rightand left teeth. The right and left sides of an animalhave the same genetic underpinnings, so the dif-ference between the sides must logically be due tonon-genetic factors (Grüneberg 1935; Van Valen1962; Palmer and Strobeck 1986). Exceptions tothis logic include directional asymmetry, consistentasymmetry in organs like the heart, and antisym-metry, consistent differences between right and leftparts like the disproportionate size of the claws ofsome crabs (Morgan 1923; Rosenberg 2002).These exceptions do not, however, pertain to differ-ences between right and left teeth, except insofaras the two sides are normally mirror images of oneanother. Difference in shape between left and rightteeth (apart from mirroring) is an example of fluctu-ating asymmetry, or inconsistent, randomly distrib-uted difference that results from the inability of theunderlying genetics to determine identical struc-tures. Leamy and Klingenberg (2005) reviewed the

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PALAEO-ELECTRONICA.ORG

genetics of fluctuating asymmetry. An estimate ofthe variance between right and left teeth relative tothe variance between the teeth of different individu-als can be thought of as a minimum estimate of E,the environmental component of variance withinthat species, because the right-left asymmetry isnon-genetic. Analysis of variance (ANOVA) can beused to mathematically partition the within-speciesvariance in tooth shape into between-individualand between-sides components, the latter being anestimate of E. This estimate of environmental vari-ance is a minimum one, however, because someenvironmental effects, like quality of diet or ambienttemperature, will affect both sides equally to theextent that they have an effect at all. But despite itsshortcomings, an estimate of E based on asymme-try can be made on fossil specimens as easily asextant ones, presuming that the left and right teethcan be associated with the same individual.

We estimated the minimum environmentalcomponent of variance using asymmetry in the out-line shape of lower first molars from four species of

arvicoline rodents. We used those estimates todetermine the likelihood that environmental effectswill result in erroneous species determinations. Wealso used the data to explore whether right and leftmolars from the same individual can be associatedbased on their shape alone.

MATERIALS AND METHODS

We measured the outline shape of the firstlower molars (Figure 1) in Arvicola terrestris, thewater vole (N = 28), Microtus agrestis, the field vole(N =24), M. arvalis, the common vole (N = 38), andM. oeconomus, the root vole (N = 14). Specimensare housed in the National Museum of Scotlandand the The Harrison Zoological Institute (Seveno-aks, England).

The right and left teeth of each individual werephotographed with a Canon 350D digital SLR cam-era with macro lens arrangement giving x2 magnifi-cation. Care was taken to orient each tooth so thatits occlusal surface was oriented horizontally, per-pendicular to the line of sight. The left tooth of each

1.1 1.2 1.3

Lingual

Anterior

AC

PL

T7

T5

T3

T1

T6

T4

T3

LRA1

LRA2

LRA3

LRA4

BRA1

BRA2

BRA3

FIGURE 1. Morphology and outlines of the first lower molar. 1.1, photograph of the occlusal surface of Microtus arva-lis. 1.2, outline of the same molar. 1.3, two hundred fifty outline coordinates running anticlockwise from the startingpoint marked by the arrow. AC, anterior cap. BRA, buccal reentrant angle. LRA, lingual reentrant angle. PL, posteriorlobe. T, triangle.

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individual was flipped to remove the effects of mir-roring. The outline of each tooth was traced usingimage processing software (Adobe PhotoshopCS2 ©). Chips in the enamel were ignored in thetracing because we did not want to include differ-ences due to breakage in our estimate of asymme-try. Two hundred fifty evenly spaced points werethen fitted to the traced outline for quantitativeanalysis. The points ran counterclockwise aroundeach outline starting at the apex of the first buccalreentrant angle (Figure 1.3).

We analyzed the coordinates using two differ-ent outline methods to ensure that choice ofmethod did not substantially affect the results.

The first method was Standard 2D Eigen-shape (Lohmann 1983; MacLeod and Rose 1993;MacLeod 1999). In Eigenshape, the outline coordi-nates are transformed to a Zahn and Roskies(1972) shape function (φ), which is a vector of netangular change the positions of neighbouring out-line coordinates beginning at an arbitrary startingposition that is the same on all objects. The func-tion was standardized by subtracting the anglesdescribing a circle of the same mean radius (φ*) asrecommended by MacLeod (1999). The tooth out-lines were ordinated in principal components (PC)space by singular value decomposition of the cova-riance matrix of the φ* functions. The PC scores ofthe tooth outlines are, by definition, uncorrelatedwith one another but preserve the shape distancesamong the original outlines and so can be used asshape variables for further statistical analysis.Eigenshape distances between tooth outlines canbe calculated either as the Euclidian distancebetween the φ* functions or as the Euclidean dis-tance between the full set of PC scores (the twodistances are identical). These distances are anal-ogous to Procrustes distances in landmark analy-sis.

The second method of shape analysis was aProcrustes-based semilandmark analysis (Book-stein 1991; Rohlf 1993; Dryden and Mardia 1998;Zelditch et al. 2004). The same 250 outline coordi-nates were treated as semilandmarks (Bookstein1997). The shapes were superimposed using Gen-eralized Procrustes Analysis (GPA, Rohlf 1990).The mean shape was subtracted from the superim-posed coordinate points. The tooth shapes wereordinated in PC space by singular value decompo-sition of the covariance matrix of the resulting Pro-crustes residuals. Like with Eigenshape, the PCscores are uncorrelated and preserve the originalshape distances and so can be used as shapevariables for further statistical analysis. Procrustes

distances between the tooth shapes can be calcu-lated either as the Euclidean distances betweentheir Procrustes superimposed coordinate points oras the Euclidean distance between the full set ofPC scores for the two teeth.

Shape variance was partitioned into between-individual and between-side components usingMultivariate Analysis of Variance (MANOVA) on thePC score shape variables with both data sets foreach of the four species. The between-individualcomponent of variance is the part that describesthe average difference between the teeth of indi-vidual voles independent of asymmetry; thebetween-side component describes the variancebetween left and right sides. The former is an esti-mate of within-species variance unbiased by thenon-genetic variance associated with fluctuatingasymmetry; the latter is a minimum estimate ofenvironmental variance, E (Palmer and Strobeck1985; Klingenberg and McIntyre 1998).

The absolute values of the variance compo-nents are rather arbitrary since the scale differsbetween Eigenshape and Procrustes analysis.However, the proportions of between-individualand between-side variances to the total variancecan be compared from one analysis to the other. Amaximum estimate of heritability (h2), which is theproportion of phenotypic variance that is passedfrom parent to offspring, can be calculated as h2 = 1 – (between-sides variance / total variance),

( Equation 2)which is the same as h2 = G/P since the

between-sides variance is a proxy for E. By Equa-tion 1, G/P = 1 – (E/P). This estimate of h2 must beconsidered a maximum because some environ-mental variance will be undetected by the analysespresented here, as mentioned above.

RESULTS AND DISCUSSION

Shape variation

Typical variation among individuals andbetween left and right teeth is illustrated in Figure2. Variation in the shape of the anterior cap is eas-ily seen between individuals, but the left and rightteeth of the same individual have the similar capshapes.

The similarity between left and right molarsmay also be seen in the PC scatterplots (Figures 3and 4). More often than not, the left and right teethof the same individual are nearest neighbours inthe plots, both for Eigenshape and semilandmarks.

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FIGURE 2. A representative sample of individual and left-right variation in the shape of the first lower molar of fourarvicoline species. Outlines of the left and right teeth of Arvicola terrestris (2.1), Microtus agrestis (2.2), M. arvalis(2.3), and M. oeconomus (2.4) are illustrated. The left tooth was flipped to facilitate comparison with the right.


MANOVA and Components of Variance

The results presented visually above can bemeasured quantitatively by partitioning shape vari-ation into between-individual and between-sidecomponents with MANOVA. Both Eigenshape andsemilandmark analyses showed that between-indi-vidual variance was much greater than variancebetween left and right teeth (Table 1). Microtusagrestis and M. oeconomus had the greatest

amount of asymmetry (22.4-28.5%), whereas Arvi-cola terrestris and M. arvalis had less (11.4-13.8%). These results suggest that within-speciesvariation is only marginally inflated by random envi-ronmental effects.

Using left-right asymmetry as a minimum esti-mate of environmental variance (E), heritability (h2)of tooth shape in the four species was estimated(Table 1). Heritabilities ranged from 0.71 to 0.89.

TABLE 1. MANOVA results for the partition of variance between individuals. The sum of squared deviations for indi-vidual differences and left/right differences is reported along with the percentage of the total variance accounted for and

the maximum estimate of h2 for each species.

Eigenshape Analysis

Source of variationSum of squared

deviationsPercentage of total

Proportion (Max h2)

Arvicola terrestris

Individual differences (between groups) 748.5 88.6% 0.89

Left and right differences (within groups) 96.4 11.4%

Microtus agrestis



Microtus arvalis



Microtus oeconomus



Semilandmark (Procrustes) Analysis

Source of variationSum of squared

deviationsPercentage of total

Proportion (Max h2)

Arvicola terrestris



Microtus agrestis



Microtus arvalis



Microtus oeconomus



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Matching Contralateral Teeth

In many cases, contralateral teeth from thesame individual were more similar to the teeth ofanother individual than to each other. Using Pro-crustes distance, which is a form of nearest-neigh-bour matching, we found that in Arvicola terrestris,twoout of 28 (7.1%) teeth did not match to theircontralateral counterpart; in Microtus agrestis 15out of 24 (62.5%) did not match; in M. arvalis 20out of 38 (52.6%) were mismatched; and in M.oeconomus four out of 14 (28.5%) were incorrectlymatched. Procrustes distances between teeth ofdifferent individuals were often larger than betweenteeth of the same individual, but many teeth of dif-ferent individuals had Procrustes distances thatwere as small as those between teeth of the sameindividual (Figure 5). Thus, teeth of the same indi-vidual cannot reliably be matched based on shapealone.

The Relative Merits of Eigenshape and Semilandmarks (Procrustes)

As discussed above, the PC plots of molarshape generated by Eigenshape andsemilandmark analyses were broadly similar. Thefact that corresponding plots had the same teeth asoutliers on each of the two PC axes indicates thatboth methods are recovering the same variation(Figure 3). For example, the right and left molars ofspecimen 00303 of Arvicola terrestris lie at one endof the first PC extracted by both methods, andspecimen 00304 lies at one end of PC2. The factthat the positive and negative ends of the axes areflipped can be ignored because shape does nothave an inherent directionality. The percentages ofwithin and between individual variation wereroughly the same regardless of which method wasused.

That the two methods yield similar results canbe further tested by comparing Eigenshape and

-10 -5 0 5 10-10

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1500L1500R1469L

1469R1475L1475R

1497L1497R1522L1522R

1535L

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1542L

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1721L1721R

1722L

1722R1723L

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909L909R910L910R

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301R302L302R303L

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PC 1 (49.5 %)

PC 2

(18.

8 %

)

PC 1 (45.3 %)

PC 2

(20.

4 %

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PC 1 (37.9 %)

PC 2

(27.

4 %

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PC 1 (56.1 %)

PC 2

(21.

5 %

)

3.1

3.2

3.3

3.4

Arvicola terrestris

Microtus agrestris

M. arvalis

M. oeconomus

FIGURE 3. Scatterplots of the first and second principal components of tooth shape based on Eigenshape analysis.Labels are centred on the point occupied by each specimen in the shape space. L, left. R, right. Left and right teeth ofthe same individual are indicated with the same colour.

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Procrustes distances between pairs of teeth (Fig-ure 6). We calculated all possible pairwise dis-tances using both methods for each of the fourspecies. The tight correlation between the two dis-tances again indicates that each is measuring thesame differences in shape and that one methodcan safely be substituted for the other.

CONCLUSIONS

The proportion of environmental varianceidentified through fluctuating asymmetry was rela-tively small (11.0%-28.5% of the total variance),implying that heritabilities (h2) of tooth shape range

from 0.71 to 0.89. These h2 values are somewhathigher than in previous studies of heritability indental characters, but not surprisingly so. Leamyand Bader (1968) found h2 values that rangedbetween 0.60 and 0.66 for the linear size of fieldmouse molars. Hlusko and Mahaney (2003) foundh2 to be as high as 0.725 for the presence of cingu-lar remnants in baboon molars, though in mostcases h2 was around 0.60 for that trait.

While the differences between contralateralteeth are often as great as between individuals ofthe same species, they were much, much smallerthan differences between species (Figure 7). In

PC 1 (41.1 %)

PC 2

(25.

1 %

)

PC 1 (44.7 %)

PC 2

(22.

9 %

)

PC 1 (41.3 %)

PC 2

(27.

4 %

)

PC 1 (59.5 %)

PC 2

(17.

0 %

)

4.1 4.2

4.3 4.4

Arvicola terrestris Microtus agrestris

M. arvalisM. oeconomus

296 L

296 R

297 L297 R

298 L298 R300 L300 R

301 L301 R302 L302 R303 L303 R

304 L304 R

305 L305 R306 L306 R

307 L

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310 R

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1500 L

1500 R1469 L1469 R

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1522 L1522 R1535 L

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1723 R1739 L

1739 R

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1750 R

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996 L996 R

773 L

773 R774 L

774 R

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909 L909 R910 L

910 R

911 L911 R

912 L912 R

914 L914 R

916 L916 R

982 L

982 R

988 L988 R

989 L

989 R

990 L990 R

991 L

991 R

992 L992 R993 L

993 R

994 L994 R

995 L995 R

-0.2 -0.1 0.0 0.1 0.2-0.2

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3091 L

3091 R

3090 L3090 R

3093 L3093 R

123 L123 R

3092 L

3092 R

909 L909 R

FIGURE 4. Scatterplots of the first and second principal components of tooth shape based on semilandmark (Pro-crustes) analysis. Labels are centred on the point occupied by each specimen in the shape space. L, left. R, right.Left and right teeth of the same individual are indicated with the same colour.

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FIGURE 5. Histograms of Procrustes distances between teeth from the same individual (black bars) and betweenteeth from different individuals (red bars). While the largest differences are between teeth from different individuals,the distribution of distances between sides overlaps with distances between individuals in all four species.

FIGURE 6. Comparison between Eigenshape and semilandmark (Procrustes) analysis. For each of the four speciesa scatterplot shows the relationship between the morphometric distance between pairs of teeth calculated usingEigenshape (y-axis) and Procrustes superimposition of semilandmarks (x-axis). R2 is the proportion of variance inProcrustes distance that is explained by Eigenshape distance.


Arvicola terrestris the maximum Procrustes dis-tance between teeth from two sides of the sameindividual was 0.015 units. The mean distancebetween teeth belonging to different species wasnearly an order of magnitude greater at 0.095units.

Arvicoline rodents may have especially vari-able teeth, and they may vary within species andbetween species, but the magnitude of variationbetween species is so much greater than thatwithin species that variation is not likely to con-found palaeontological interpretations. The amountof ecophenotypic environmental variance withinthe species we measured appears to be negligiblecompared to the differences we observed betweenspecies.

ACKNOWLEDGMENTS

N. MacLeod and J. Krieger provided helpfuladvice on Eigenshape Analysis. The Harrison Zoo-logical Institute and Scottish Museum of NaturalHistory graciously provided access to specimens.This research was supported by the Ancient Britainin its European Context project (AHOBII), which is

funded by a research program grant from theLeverhulme Trust.

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